Faculty of Mechatronics, Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Warsaw, Poland.
Faculty of Mechatronics, Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Warsaw, Poland.
Comput Methods Programs Biomed. 2022 Apr;216:106669. doi: 10.1016/j.cmpb.2022.106669. Epub 2022 Jan 29.
Causality defined by Granger in 1969 is a widely used concept, particularly in neuroscience and economics. As there is an increasing interest in nonlinear causality research, a Python package with a neural-network-based causality analysis approach was created. It allows performing causality tests using neural networks based on Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), or Multilayer Perceptron (MLP). The aim of this paper is to present the nonlinear method for causality analysis and the created Python package.
The created functions with the autoregressive (AR) and Generalized Radial Basis Functions (GRBF) neural network models were tested on simulated signals in two cases: with nonlinear dependency and with absence of causality from Y to X signal. The train-test split (70/30) was used. Errors obtained on the test set were compared using the Wilcoxon signed-rank test to determine the presence of the causality. For the chosen model, the proposed method of study the change of causality over time was presented.
In the case when X was a polynomial of Y, nonlinear methods were able to detect the causality, while the AR model did not manage to indicate it. The best results (in terms of the prediction accuracy) were obtained for the MLP for the lag of 150 (MSE equal to 0.011, compared to 0.041 and 0.036 for AR and GRBF, respectively). When there was no causality between the signals, none of the proposed and AR models did indicate false causality, while it was detected by GRBF models in one case. Only the proposed models gave the expected results in each of the tested scenarios.
The proposed method appeared to be superior to the compared methods. They were able to detect non-linear causality, make accurate forecasting and not indicate false causality. The created package enables easy usage of neural networks to study the causal relationship between signals. The neural-networks-based approach is a suitable method that allows the detection of a nonlinear causal relationship, which cannot be detected by the classical Granger method. Unlike other similar tools, the package allows for the study of changes in causality over time.
1969 年，格兰杰提出的因果关系概念得到了广泛应用，尤其是在神经科学和经济学领域。随着人们对非线性因果关系研究的兴趣日益增加，我们创建了一个基于神经网络的因果分析方法的 Python 包。它允许使用基于长短期记忆（LSTM）、门控循环单元（GRU）或多层感知器（MLP）的神经网络进行因果检验。本文旨在介绍非线性因果分析方法和创建的 Python 包。
在两种情况下，使用自回归（AR）和广义径向基函数（GRBF）神经网络模型的创建函数对模拟信号进行了测试：信号之间存在非线性依赖关系，以及 Y 信号到 X 信号不存在因果关系。采用 70/30 的训练-测试分割。使用 Wilcoxon 符号秩检验比较测试集上的误差，以确定因果关系的存在。对于选定的模型，提出了一种随时间变化研究因果关系变化的方法。
当 X 是 Y 的多项式时，非线性方法能够检测到因果关系，而 AR 模型无法指示。对于滞后 150 的 MLP，得到了最佳的结果（在预测精度方面）（MSE 等于 0.011，而 AR 和 GRBF 分别为 0.041 和 0.036）。当信号之间不存在因果关系时，所提出的和 AR 模型都没有指示虚假的因果关系，而 GRBF 模型在一种情况下检测到了虚假的因果关系。只有所提出的模型在每个测试场景中都给出了预期的结果。
所提出的方法明显优于比较方法。它们能够检测非线性因果关系，进行准确的预测，并且不会指示虚假的因果关系。创建的包使使用神经网络研究信号之间的因果关系变得容易。基于神经网络的方法是一种合适的方法，它允许检测经典格兰杰方法无法检测到的非线性因果关系。与其他类似的工具不同，该包允许研究因果关系随时间的变化。
